I have a real plant that I'm sampling with 0.001 interval. For this reason all the measurement data in my Matlab are vectors that include data from every 1ms.
I have also constructed a state-space model for my real plant and I want to do greybox-modelling and thus identify some parameters of my real plant by using the measurement data.
I'm wondering now, should I do the parameter identification for a continuous-time state-space model of the plant, or for a discrete state-space model (discretized with 1ms sample time)? The real world is continuous, but the measurements from the plant are "discrete" as I have them only with 1ms interval. Thus, which is better, to use the measurement data to identify parameters for a continuous or discrete time state-space model?
Additionally, I do a idgrey model of my state-space model. Should I construct this idgrey model based on continuous-time model of the plant, or discretized model of the plant? The discrete-time idgrey model needs the "sampletime Ts" as input in order to produce the idgray object. Does the idgray-function discretize the model with the given sampletime and return the discretized grey-box model? Or is the "Ts" only used for metadata that is included into the idgrey object's data?
Thanks for any ideas for declaring this.